A power-transmitting clutch can include an input shaft and an output shaft rotatable about a common axis. At least three members can be supported thereby in an array of adjacent members spaced along the axis and co-axial with the shafts. The outer of the members can have surfaces facing opposite surfaces of one or more intermediate members. One of the members can be constrained to rotate with one of the shafts, while another of the members can be constrained to rotate with the other of the shafts while being movable along the common axis. The clutch can also have a mechanism for moving the members toward one another for mutual engagement of the facing surfaces, whereby the input shaft transmits rotation to the output shaft when the facing surfaces are mutually engaged. The mechanism can transmit rotational force from an input shaft to a member supported thereby, or can transmit rotational force from another member to an output shaft that supports the other member. The mechanism simultaneously permits movement of either member relative to the corresponding supporting shaft. The mechanism can include portions integral with or secured to either shaft extending along or parallel to the axis of rotation thereof which portions connect the member to the corresponding supporting shaft for rotation and permit movement only in a direction parallel to the axis. The portions of the mechanism can include gear-like teeth and grooves in the shaft or drum mating with complementary grooves and teeth in the member, which can also be described as ribs or slots in the shaft or drum mating with complementary slots and protrusions in the member. A plurality of first members can be in torque-transmitting connection with an input shaft, a plurality of second members can be in torque-transmitting connection with an output shaft coaxial with the input shaft, and wherein the first and second members alternate with one another along the axis of the shafts.